The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  X 2X  X  0  X  0  X  X  X 2X+2  X  2  X 2X+2  X 2X+2  X  X  0  X  2  X  X  0  X 2X  2  X  0  X  X  X  1  1  1  2  1
 0  X  0 3X+2  2 X+2 2X+2  X  0 3X+2  0 X+2  2  X 2X+2  X 2X 3X+2 2X X+2 2X 3X+2 2X X+2 2X+2 3X  2 3X 2X+2 3X  2 3X X+2  X X+2  X 3X+2  X 3X+2  X 2X  2  X  X 3X  X  X  X  X  X  0 2X+2  0 3X  X X+2 X+2  X  2  X  2 3X  X 2X+2  0 2X 2X  2 2X+2 2X 2X
 0  0 2X+2  2  2 2X 2X 2X+2 2X 2X+2  2  0 2X+2  2  0 2X 2X 2X  2 2X+2  0  0 2X+2  2 2X+2 2X+2 2X  0  2  2  0 2X  0  2 2X 2X+2  2  0 2X+2 2X  2  2  2  0  0  2 2X 2X+2 2X+2 2X  2  2  2 2X 2X+2 2X+2  2  2 2X+2 2X 2X+2  2 2X+2 2X 2X+2  0  2 2X+2 2X+2 2X+2 2X+2

generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+146x^69+85x^70+136x^71+9x^72+60x^73+24x^74+40x^75+4x^76+2x^77+2x^78+1x^80+1x^86+1x^88

The gray image is a code over GF(2) with n=568, k=9 and d=276.
This code was found by Heurico 1.16 in 6.48 seconds.